{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 线性支持向量机的朴素实现\n",
    "\n",
    "+ 虽然从形式上来说，线性支持向量机（LinearSVM）和感知机的差别只在于损失函数，但如果只是简单地将感知机的训练策略（亦即每次只选出使得损失函数最大的样本点来进行梯度下降）迁移过来的话、会引发一些问题。为方便，我们称感知机的训练策略为`极大梯度下降法`（注：这不是被广泛承认的称谓，只是本文的一个代称）\n",
    "+ 我们会先展示极大梯度下降法的有效性，然后会展示极大梯度下降法存在的问题，最后则会介绍一种解决方案、并将该解决方案拓展为 Mini-Batch 梯度下降法（MBGD）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 极大梯度下降法训练 LinearSVM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "class LinearSVM:\n",
    "    def __init__(self):\n",
    "        self._w = self._b = None\n",
    "        \n",
    "    def fit(self, x, y, c=1, lr=0.01, epoch=10000):\n",
    "        x, y = np.asarray(x, np.float32), np.asarray(y, np.float32)\n",
    "        self._w = np.zeros(x.shape[1])\n",
    "        self._b = 0.\n",
    "        for _ in range(epoch):\n",
    "            self._w *= 1 - lr\n",
    "            err = 1 - y * self.predict(x, True)\n",
    "            idx = np.argmax(err)\n",
    "            # 注意即使所有 x, y 都满足 w·x + b >= 1\n",
    "            # 由于损失里面有一个 w 的模长平方\n",
    "            # 所以仍然不能终止训练，只能截断当前的梯度下降\n",
    "            if err[idx] <= 0:\n",
    "                continue\n",
    "            delta = lr * c * y[idx]\n",
    "            self._w += delta * x[idx]\n",
    "            self._b += delta\n",
    "    \n",
    "    def predict(self, x, raw=False):\n",
    "        x = np.asarray(x, np.float32)\n",
    "        y_pred = x.dot(self._w) + self._b\n",
    "        if raw:\n",
    "            return y_pred\n",
    "        return np.sign(y_pred).astype(np.float32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 测试"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "准确率：   100.0 %\n"
     ]
    }
   ],
   "source": [
    "from Util import gen_two_clusters\n",
    "\n",
    "x, y = gen_two_clusters()\n",
    "svm = LinearSVM()\n",
    "svm.fit(x, y)\n",
    "print(\"准确率：{:8.6} %\".format((svm.predict(x) == y).mean() * 100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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X2hyxhDKcRIaTWGFeuKp0Is5RuVEWIwZuZADnu4icK7t+eTQg0RF5m1DpRjwd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\n45Vaft8FcGLtnK+p0sRZL9+bADXbQpPr826sgpz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kH4WlT+QtuaQdhsWj4Zo34dTm0uqY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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cfb373b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Fb10jsfKilIVnaRi4+z0UFeODitgVU4bhRO6+ukZKH36e0keeH5GoD0bOe584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\nsCulVI35/3GJTZsbAlWNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cfb39d6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from Util import visualize2d\n",
    "\n",
    "visualize2d(svm, x, y)\n",
    "visualize2d(svm, x, y, True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 可视化训练过程\n",
    "\n",
    "+ 实现思路如下：\n",
    "    + 在每一步迭代时生成一张如上所示的图像\n",
    "    + 在最后调用相应的第三方库（`imageio`）、将生成的所有图像合成一个 mp4\n",
    "    + 用`ffmpeg`将 mp4 转为方便分享的 gif\n",
    "\n",
    "![LinearSVM](https://cdn.rawgit.com/carefree0910/Resources/f0978da2/Lines/LinearSVM.gif)\n",
    "\n",
    "![LinearSVM](https://cdn.rawgit.com/carefree0910/Resources/f0978da2/Backgrounds/LinearSVM.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 存在的问题\n",
    "\n",
    "+ 由上述可视化其实已经可以看出，用极大梯度下降法训练 LinearSVM 会非常不稳定\n",
    "+ 从直观上来说，由于 LinearSVM 的损失函数比感知机要更复杂，所以相应的函数形状也会更复杂。这意味着当数据集稍微差一点的时候，直接单纯地应用极大梯度下降法可能会导致一些问题——比如说模型会卡在某个很奇怪的地方无法自拔（什么鬼）\n",
    "\n",
    "可以通过下面这个栗子来直观感受一下 LinearSVM 存在的这些问题："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "准确率：    50.0 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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4hyOAWrBspp1n2M6DrAqZrSGRtPTC1DSOKFYwiZVMCvuYEcSGXMxdw7Qujy2g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\notAh+BJESfMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cfd6b2748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qoSq6rRMqxAbGUKWExtc8VD/nQws4hJ9Rx5y0u+fIp9YpjeWQQhLOxUikx/cV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\n0I0xpkH8PxY7WAsKiA2VAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cfd667748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 注意我们只是把 center 参数（亦即正负样本点的“中心”）\n",
    "# 从原点(0, 0)（默认值）挪到(5, 5)（亦即破坏了一定的对称性）、\n",
    "# 并将正负样本点之间的距离（dis 参数）稍微拉近了一点而已，\n",
    "# 结果就已经惨不忍睹了\n",
    "x, y = gen_two_clusters(center=5, dis=1)\n",
    "svm = LinearSVM()\n",
    "svm.fit(x, y)\n",
    "print(\"准确率：{:8.6} %\".format((svm.predict(x) == y).mean() * 100))\n",
    "visualize2d(svm, x, y)\n",
    "visualize2d(svm, x, y, True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通过下面这张动图，我们能够直观地感受极大梯度下降法下 LinearSVM 的训练过程：\n",
    "\n",
    "![Failure of LinearSVM][1]\n",
    "\n",
    "可以看到，LinearSVM 确实卡在了奇怪的地方\n",
    "\n",
    "原理我不敢乱说，这里只提供一个牵强附会的直观解释：\n",
    "\n",
    "+ 每次只取使得损失函数极大的一个样本进行梯度下降$\\rightarrow$模型在某个地方可能来来回回都只受那么几个样本的影响$\\rightarrow$死循环（什么鬼！）\n",
    "\n",
    "专业的理论就留待专业的观众老爷补充吧 ( σ'ω')σ\n",
    "\n",
    "[1]: https://cdn.rawgit.com/carefree0910/Resources/83441596/Lines/LinearSVM(Failed1).gif"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 解决方案\n",
    "\n",
    "极大梯度下降法的最大问题很有可能在于它每次都只根据**使得损失函数最大的一个样本点**来进行梯度下降，这会导致两个问题：\n",
    "+ 模型的训练将会很不稳定（这点和随机梯度下降类似）\n",
    "+ 模型对噪声或“不太好的点”极为敏感（因为它们往往会使损失函数最大）\n",
    "\n",
    "按部就班、我们先解决第一个问题，为此我们只需要多选出几个样本点（比如选出使得损失函数最大的 top n 个样本）、然后取它们梯度的平均即可\n",
    "\n",
    "### Top n 梯度下降法\n",
    "\n",
    "+ 注：该名字同样只是我瞎编的一个名字（喂）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 继承上一个 LinearSVM 以重复利用代码\n",
    "class LinearSVM2(LinearSVM):    \n",
    "    # 用参数 batch_size 表示 Top n 中的 n\n",
    "    def fit(self, x, y, c=1, lr=0.01, batch_size=128, epoch=10000):\n",
    "        x, y = np.asarray(x, np.float32), np.asarray(y, np.float32)\n",
    "        # 如果 batch_size 设得比样本总数还多、则将其改为样本总数\n",
    "        batch_size = min(batch_size, len(y))\n",
    "        self._w = np.zeros(x.shape[1])\n",
    "        self._b = 0.\n",
    "        for _ in range(epoch):\n",
    "            self._w *= 1 - lr\n",
    "            err = 1 - y * self.predict(x, True)\n",
    "            # 利用 argsort 函数直接取出 Top n\n",
    "            # 注意 argsort 的结果是从小到大的，所以要用 [::-1] 把结果翻转一下\n",
    "            batch = np.argsort(err)[-batch_size:][::-1]\n",
    "            err = err[batch]\n",
    "            if err[0] <= 0:\n",
    "                continue\n",
    "            # 注意这里我们只能利用误分类的样本做梯度下降\n",
    "            # 因为被正确分类的样本处、这一部分的梯度为 0\n",
    "            mask = err > 0\n",
    "            batch = batch[mask]\n",
    "            # 取各梯度平均并做一步梯度下降\n",
    "            delta = lr * c * y[batch]\n",
    "            self._w += np.mean(delta[..., None] * x[batch], axis=0)\n",
    "            self._b += np.mean(delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 测试"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "准确率：    92.5 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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ffEwUY8GCFRMWIklhf4XPQ2KPXKHXkIJ0iNluP0zYlA/7/gcjH3FOXA1Nl1Hw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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cfd6d8c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LiAmE20LPtsj/6vAWixTpKbjCT7xN4P+PLyHcJT/IhM8dAa0OW+OjGvKaLYgf\nbtqnBTQhJWX3P0npA6uwXIY9e0yxX8mDT1Nz7hkJC6giHKHkgeSqz4GoueATNJ94VFoR7UFKtGCY\ngqfW0jFvpp2r3lf8hUC6jZ4la//COTScfizFj78w4DgEMPnGO2lbchjNxy8mMHOK/fbTva4Qi+Ns\naSfrnY09x9SdfSL1Z5/U8z2EK0poOe5IZl77f4PqmqRHoui1e3vICmDy7+9iyzWXIg2nfW0p0YMh\n8p9/fcDzHezs8zuMECILOBa4FUBKGZVSDn41ZgLjWRhl8gP15F7Qge/kIAVXtjP5gXocuWoFfjSJ\nbjWS1i741BGw2wUdTvA7IazDL6ch/2sW/t3HpzyPxPZ0sVIsknYjLAs9jZgDFDz9CqX3PYneEYCu\nGXv5XY+SP8RZZDQ/xy6570/MpbR90rfsYs5VP0eTktIHVkHflM0UrovSZdC8IoV5VxqElOS++g7T\nf/435l75M3JfeQcRjkA8jpAW8Wwfuy/5FHGfl3iGh/pzViQ81KTLIJqXTfMJRw76mn3x7NjTVXjV\ndS9CYGZ42fa9S1J60ij2MpwZ+lSgEfi7EOIw4C3gSill+pWlAwhnqUnhN/3jPYyDCtfUGOH3e4n6\n9E6ocYPsMy8JOuC306nLuYzsiucTPvIfOovdl3yaeG4WSEnuy29Rcft/EkrhB4MAilatpfDpl21X\nw0h0n+xhO2dPQZgmEmf6nWJx5n7n5xgt9s9bNC8bEY2R9c5H+BfP3ztLTxPX77tAPFic/k6q/nwP\n0aIrCE6pQBoGpmHQcuxiOufNoPzOR2xTLiNx7NJl4F84l6Kn1u7TdVuXLbSrcHvFzKXhJDypjMDM\nyfi6CsAUyQxH0B3A4cA3pZSvCyFuBK4B/rv3TkKIy4DLAApKyodxOcXBTu75nfif8CK7Bf2kJrg7\nTdGJqRELliRsCk4pZ/tVFyUU47QuOxzT62HKjXcm7BvpqKR9zwkIPUZOxTM4PY2kQkg5rG72zvZO\nUk47pQRpp2BW3P4QRoufWE4m26+8kFBXdaeVrutRb+Jxst76oP99+iEwa7LdZ7S3aDsdxLMyCVWV\npo73mxbO1n2f7ASnVqTsniSFIFxVpgS9H4azbFwNVEspuwNbD2ALfAJSypullIuklIsyc/OGcTnF\nwY4xJU7575twToqBQ8KMQGoxBMAio3Bdwpb6s05IKgrqnk3GcvYac9V9eBkfPfkINe9+hz1vX82H\njz5Ny46yIz3kAAAgAElEQVQzEo4zXQaNJy9l+7cvpPr8MwlOKh9yfrZlOInk54AmktMFhQDTpPIv\n95L/whtIYOs1lxGcVoU0nHaIJp2Yd51LhKM4/Z0p3RwHS2hSOVJPvo7lcRHL8uFsbe9JA+1BEwSn\nVdK+YM4+XdO9pyGplR/YYTCjXrWx6499nqFLKeuEELuFELOklB8DJwHJ7j8KxQjiPSLK5AfrsToF\n4QKdPfkfwlfnQ1Swt32OBC/k3LQI7tt7bKSsKOWMUsTiRPNzcLZ1EGydRd2HlyPNxPTDXW9cT2bJ\nKzjdrcQzPGz66beJZfns+LGUNK08DhGPU/D0K5Td+/iAXuDR3Cw2/e+VWB63Lc6pUvV0Df8Rh5D3\n2ruEJpcTLcpL2YA5AcvCqGvCs6sW38Zt5K1ZN2DGSX8YDS2IuIXsE7UR4QjumkaKn3iJbd+7hHBx\nARiOniKoSHkxO678IpU330/eq+8M6Zq5a9+i7jOnYlqOvf9ecRNnWweZH2ze53s5GBhuYuc3gbuF\nEO8BC4CfDX9ICkX/CAF6psQbySD7zCDilVfgtAbIi0J+BOOTLUz+Zz1GVTzB4Mu7eWfqvplOB66u\nTIvWnSuRZnI8W2Dh33MCAA2fONG24e1eDOwSMel00nTyUqq/ePaA97DnonOIZ/v2hhbSeLSbPjtx\nLJaTlbL5ctI4Y3Em//4uptx0J4VPvzwsMQe7SYajM5A4C7cstLhJ3svrMZpamX3Nb3DXNqRckK05\n/6whL2Q6gmFmXPd7vFt22teNm2S9u5Hp//NH1f1oAIaVtiilfAdYNEJjUSiGhEBQtLuCrMwAnbfv\nQMidZLbm4Qonzq4DV68mss2B9qv/wBIBmtUz8xPhKAXPvLzXzlZqpGqUKQEp7dlx25HzkxYCe/Zz\nGbQcfyRl9zzeb2zdv3BOcuPlvvcXjpDz+nsAeLftRjpS/LrG44hoHAwnnh3VlN/5yD5Z0EqwC4Y0\nDdee+p5vQEjJjOv+yK7LP0/H3OmAnYUy6S/39jTIALsBRyri2T4slzHkdQZ3TSMzr/sjltNhp2um\neBArklHmXIr9HisCnc94CW9w4pwcJ+v0ILqvK06MwBPw4Qmk99FpucNH820ZyL8tBkc9wuqyEoib\n5KxdR+k9T/Tsm1O1isbN5yNNT+JJpE52+QuAXaLeH8Ky0/v0Pn7sCadLN9vuSj3UwhFcNQ3kvrwe\nsDNOClatpWnFsp43AxGN4fB3MvsHv9nbfYj0vZvTEaoqZftVFxHLzkIg0QMhJt90Z4+vurPNz7Qb\n/oZlOJGa1tOmz9J14lkZOPwBnK3tREqLks6tRWIDVp/2x1Czjw52lKArxpxYnU7b/RlEtjjxHBIl\n+7MBHHmpBS7eqrHrwiLMFg0Zst0Zm/+YRdXtjRiTB/5lj+3Raf5TNvKm9+HMBoSr+5VdgNNB63GL\niRXmM+2XtyCkxJO9mYz89XQ2LLH3wUToJhULb+jJdClY9TJ7Ljw7ZR9PAKQcsGI0Y9MOAvNmJIda\nhED3d1J2z+Pkvrw+YWZads/jeHbsoe4zpxDLy0EPhMh/5lVEPE4sy0f1xefgX3QIUgiy3tlI/rOv\nESkrxNnqJ3vdBynF0TKcbPmvr9mWBZqGxO6xuvWaS5l75c9w9DIA6xZmCdSffSINnzgRqWkIS+J7\n5yMieTnQp19q4ZMvqjDJGKIEXTGmhDc62f2VQmTMrrINveGi9Z5Mqu6sx6hMfq1u+n0W8Xod4rbw\nybCGjEjqrsul6vbUqYS96XzJA04TLtyD8KR4aDidBGdNpu3IQ8l+eSMfr76XaEcVoGPnDULhjDso\nmLF3dTX/xTcJTq+i5ZgjoDsM0iXMIhyh+MHVA4YIyu55nM3Xfzt5Kh2Lk//CGyl7mwogOH0S8dxs\npMsg7jKoP+dk2o+cT9zrIVaQ0zMe/+Fz8R/ey0QrHmfaz/9GZp+uTG2L59nZOX3NsDSN1mULKXz6\n5aRxNJ26PKE6VAIdC+eQ9fZHBObNwDKcCMui4Mk1lDz4TL/fg2JkUYKuGFPqr89FBnsVjEQ1ZFzS\n+Jscyn/XnLR/57PeHjHfe5Ag/KGBFRJongGcGjUJPhO09PtZbhdtSw8jftcsIh1VSLPbwUKAdNK4\n+UKKD7kVh2HnVgspqbrlAYr/8yytSxbQvuRQwiUF6JEYjo4AwemT6Jg3o9+MjIwde8h6ewP+Q2ft\nNdmyLNsgLIWIAkQKcmk+aUlC/F66DLu3KXLvwwWSZ/4OB1uv/Srzv/wj9F4z9Xh2FlaK2Lw0nAmp\nnL3pLeY9+7tdBOdMZd7l1xH3edEDoSQfHcXoo+zLFGOGjEFkY4rFREsQfD11+EI40gixhJbbfLQ9\nmIHZkT5i7DsxBG1OqO3HBVFKQrnltLWc1EvMe41BixFoXJi03dXUSsljzzPzJ7/Hs7sOy+MiXFVK\n+1GHsu07F1PzmVPTXxOYfNOdFK5+GS0YBtMkY+M2Zlz3B4w04ZrOOVNTtoSThjP1gmnCTdh+6k2n\nJvZUzdi0HZFCeLVwFN/G1I2f41mpbaLjmT6EZeH0dyoxHyfUDF0xdmi2F3rKvqICWu/y4TsliLNo\n7w6ZZwRpvz8DGe0tZBIsaLk1C9ySpt9lU3FzI+7ZyYtvjkKLomvbaLhyLtzzNnis5DCHEESrCog9\nFIbDY2A6ITcKF1fDvA7k227EzvSOFm2L5hOeVJbgxyLdLhrPPJ7CZ17F2Za6alKLxSm/61HK73o0\n7bl7E5xamdpCVkq7G9NA0zMhCE5NrKz1btlF5odb6Dhk+t7F1kgUz849ZPZymOyN0dCSMqvFVdsw\nqPtQjB5qhq4YM4QOmacHEc6+ii6REUHTH7LYcXYJ/lV7M0wKvubHNTMGbquryUV3DkfXf2ENq1NQ\n+4O8tL0Zss8KMuUbFjm3H4JzWxZYJFeYuiTWFAtxTg3M6oQtL8D/foy4pBpu2MquO1am7RfafsQh\nKc21hGnSOXda0nYJNB1/JBtv+C4f3vQjdl/8SWIprHj70jlnavrq0L7Vpqm+DClpXzSf3V86p6dH\nqACm/N8/KL/rUTzbduPesYfS+55k2s/+mnIxs+H0Y+zvoc9nIhKl/M5HBrwHxeiiZuiKMaXo6jZi\n1TrhDYYdog51CbO0m4cA1P0oj44nw2SeEiRzRYjKfzTSdm8Gjb/LgVgqQRPEG3Rie3SMisRXfYkk\n5AtgZVnkFWVQ6J/Cjr8GiF6ytVfGS9dZMk2cF7YSy9kN2TF7XRQgQxI3M9hzwSeYclOi5wuAw99p\nF8D0zSuXoAeSPfKrLz6H1mMX9TwEmk9YQvvi+cz+/q9xpNi/53TOfgy8UtjoJiEEOHRajlmMs7md\nkkeeszdbFgXPvUbBc6+lPz+2KVjt51dC3xx806L8zkfIeu/jfo9XjD5qhq4YU7QMSeUtTVTd0YD7\nsEjqhGkLAi95qPtxHpuPLmfXFwuJbnOmbUPXTW8NizdrNDwHW6d+RE3Vduom7WT7/A9py2/C0WFA\nJMWPflDDnSdgefteMe9G1+1ioBTkP/86om9Wi2Uh4nEyP0gMW8Rysmg5/sjEGb3Tgen1DNhiLfe1\ndxCpcrqH2D5Kug2aTj9mSMcA+BfOTdNzFKKFI+PTJLEzb7ZefQlbrrmUluWHp1w3UKRGzdAV44Jr\nehyj3CT1fLRLoCwBFkQ2uIhsdiJEOi8uiaPExFlui2robYPqb+fBtufsmXYvmipqKJyfRSikIzNM\nRG/hNgX5niw6pEj58NDiqfPePXvqqbzlAXZ/+TMIy+wpDJr2i1uSPF2CU8rTWs52zJ1O8aOJdr+9\nKXrsBdoWH0qsIAfL7UJEY7bZ2D70AzQzht6LRpgmQsrkfwNL9iysSqBj/kxaly20vdXXvoVvw9ZB\nFzrtvvSztC1d0PPAC86cTOvShUz59W00nX4MDWcch+nLwLO9mvI7HyZj6+4h38eBjBL0CYjZIWi7\nx0fnCx70XIvcL3SQcfTwPDvGg8zTg/gf9yIH04s1piETYuiJFH3P7q0iLai5Jh+5rBmcMmlPiSS8\nqIHcvx9C62lb9jo2Nroo+mgSzmInvrYsOnPaE95fRTRG7kvrSEfey+vJXvcBwRmT0CJRvFt2pYxB\nO1vaUy9smiauhv6dBPVQhFnX/pa2JYfROXc6RmMLHbOnEpg7fcj9Nj1bd6X9LEmU17xF5kdbyX7r\nA6ov+mTS/sI0ye0y4OoR5K4HVtuSw8h7/nUqBhFfD1WU0LpsYYK9seV2EZgzlZ3fvAD/gtk9C7fB\nmZPZ+qPLmfHj3+Pp0xLvYEYJ+gTD7BDsPK8Ys0nryfwIvW2Qd5mf/Is7x3l0YEUh9Lb9S+dZGEHr\np7eCZ2GU7M8EaP9Xht3Oz4R+i9Zl6s+FWxJvtKfa0e0OrE4BWWmqSDWwHCbFKyxyW6bRcSeIDIvM\nGaAV2+cuqq4g6o4Qc0XpfoC4otmU3v9Uv/euR6IDugF6dtbgqm0kVFmSkDcu4iaFq1LnnycMP26S\nt3Y9eWttS4C8vGzbtdHtso2+uh8iQkDctHuLgh3f1zUwTbRYvF+BTSXK+c++Svndj1H1l/vYdfnn\nu2bqAjRB6X1P4t5TT3BqJa1LFyTkqFtuF80nLqHguddx76nv9946D5me8m3DMpy0L56XtEZhOZ3U\nn3Myk39/14Df28GCEvQJRvu/MzCbtYQ0PhnWaPlrNjmfDqBnjl+ZdeBVF7U/yN8bFxFQ+otmMpam\nfnsQAoq+00722QE6X3TT8vcs7H5X/Yi6QyYVGsmwoOnvGUQXNuHM1u3rv5APruT8SBHT8LXZ2Sp6\ntiRncfL1dNNB1cczCWcEiLoiuMJuXEEv4W89TsavViTsGw0WEWhchG60kVn8GkLr3xFRANNu+Bs7\nvnE+gdlTwbLQAyGqbr4fd83Q0/6MlnbmXvVz2o46jFBFMUZTK9H8HIIzJ+OqbaToiZeQmqD+7JMI\nV5bg2b6H4keeS3utwLTUotx08jLyn3+D3NffJXPDZtqPmIfUdbLe3tCTN99+2OyUpmVS0/AfNntA\nQdc7gwjTSgrpCNNCSpm86KxrhCarpjm9UYI+wehc40GmWNATTklkg4H3qPEJvZitGjXfzUeGE8dW\n8918pjxe12+/Vde0OK5pnfiWR6j+egGmX3SJdh9hT2tOKDB3u2g9fyqsfRUqSmCLF34yA/njLeAx\nERrITh3WZxFfXQafCtKR00ZrcQNxRwxvRyb5dcU4o1252GlMvwJXrybjVyuQEmre/Q6NH1+I0Ow4\nveYIMuOki3FnpS7I6cbREWD6z28mnunFdLsxmlqH5XeiRWPkrUkfDgKY/Ie7B3Uu/4I5qZ0khcC/\nYDbumgYcHUHyX3gjaRc9EkXETaSR+DMgTHNAQzOA7HUfUP2lTyV/YFmp1wksC9cAD4mDDbV8PMFw\nFJopF+ykCfo4NqnuWO1J/YGEzqfTfNYH18wYU5+qJWtlmtQ9EzKODSHcqRLJgbAGN0yDB9ch8uLw\nf1Ph1MVwVzny4WK4fB7ypCU0/jKH6ppW6sp3E/GGMI04HXmt7Jq1iZhzYJvXwNWraThqDY2bLkBa\nLqy4DyvuIx4uYOsLf02bD98XR0cQV2PLsM2rTI+b4NTKAXPZJRCYVkXL8sMJppnZ6uFIyspRLGtA\nUc557Z00WTCCnDff6/dYsB8I037xN/T2TrRQGC0YRguEmHLjHeS/tA7Rx4JXxOKUPKS8YnqjZugT\njNzzOgm85E5cSNQlzoo4xox9tykdLmaHZhtu9UHGBGbn4OcNwgGZpwTpeMaDDCaeT3gl2WcFyb2g\ngz1fK0RG+lzP0uDtLHgxH3lmLdqj5Vgv58PL+Yn7ZcQInlCNMHo9AAVYmkVrcQNF1Wn6lPai5Q5f\nUlcj0IiFCwi1zsGb91HK4+KRHMyYD8NbM2B4ZiAkUPv5lTSefgwiHkc6HGS/9SFVf7k3yVnR9LjZ\n+sPLCFcUg5RIIfBu2820X96aYG+b8+o71KayLBCCnDff73c8Rks7VX++l11fO3dvdo8mmHTTXTg6\ngv0e203G5p3M+/r/EJxehaXrSKeD4PRJeHbWkB+O0HLSEiy3C1dNAxW3P4R3e/WgznuwoAR9guE5\nLErR99to+FWOHUYwwZgcp+x3TfuSvTZiZCwJ03Jr5t4Gzl0IQ5KxJJzmqNR4l0QwquJEtzl61gqE\n08JZFidjeRgrIECm6vBjwU4P/GA2BB1YWpqsmNkBiGnYJaO9j4eAPjjhiW5O0+DCcmL19VIH4tEs\ndr7ySzrqlyCEieYIUbH4J+RWPjuo66Wi+cSjaDz1aNvLpStM0n74XKov/CRVtz6QsG/1hWcTqipN\nCKcEp0+i5tyVVNzxcM82o6Wdqr/ex66vfn6fRDn3jffIeu9jOubPACnJfH/zkJtbCCnxbKtm2zWX\nEpxaieVy2g8dSzLt+r/g3VmDGET3poMRJegTkOxPBsk8LUhkk4GebWFMGr8mALEaneabswi+4UK4\npN24oVuEPRa+40O4Dxnam4PQoPKWRppvzsL/hBekneKYf5kfoYOeJcn6RAD/Y94+MXsBMSDaFWy3\nBClDMzVuMJIFQVoQf82HlQdaGqvzbqxAmrcOqePJ/TBp87aX/kCw+TCkZdie46aXna/+ClfGBXjz\n9q0Vb8OZJyS7HroMWo85gop/PNRj4SuBtmULkipNpeGk5dhFCYIOkPvau2S9u5GOeTO7RHnTkERZ\nD0fIefODfbqnbppWLCUwvaonhbE7L33Hty9k7pWq02U6lKBPUDQ3eA4d2sxnpInV6ew8rxgrKKBr\nZi4MiWNKDKMqTtZZAXzHD2123o3mlRR+u53Cb6d2Hiz6QRt6nknbvT6sDg0O9cP7mV0t5Hpji7rm\nk3tn9rVueLYAeVJTokd6SIP/m0rwTPAd2/+4hVciA6nK62NoemKsOdwxiWDLPKSVmMMpTYOGjV9i\n8rKr+71WOszMNMVBmsByGWjxrrUIIZBp2t2lc2nUQ5EBQyyjScuxixPy0bsxMzOIlBXirhnYC/9g\nRC2KHqBYUeh4zk3bAxlEto3Oc7vldh9WaK+Yg+3HEq/VKf1pC5knhhGj9BMmdCi4vIPpL9Qybf0u\niv6zA9JZnbgkZb9uJvuznYjuVMZzF8JjRXbDjICObHTClw9FvJqHjIEVFNTfkM2WY8vYfHQZNT/M\nI96492ZyPhVInuU7LbI/HU0KfcWCRT2ZMInoRDoHjtenw6hrTrkI6WjrSPCQEVKSsXF7cpNp00zr\nqDhUTLeLzllTCJcVjsj50iFJWy6sQM3QD0giWx1UX2p3BZImIMG3IkTJda0jKrCht9zJzSewxTa6\nw4F77ugu0ka2OYjtceCaESNH5hM+JYT/KW+igZfTIuu0EN4jI7jnRwm/5yK604EMOOBzh9sFSHkx\n2OUBSyBdFp7FEXZ/tYDoZmdPDL9zlYfgKy6mPFGHniHJv6Kd6A6HHWpygIzbhVKFV7UT8KxOyFf3\n5GxCmsmzTaFFyCzu3xArHabHTaiyODmdT0oKVq1NyuSvvO0BNv/PN7EcDqTLQESiaJEo5X3CLftC\nw6nLqT13JcI0kbqOe08DU391K872jn0+Z/4Lb1Bz7sqkkJKzvQNXrZqdp0MJ+jhhhQSx3Q70QrPf\nHO2hIiXUXFWA2ZbYvb7zWQ8dR0XIOmPgha3INgct/8gkusWJ+5AouRd2JLkYAjhK40S3Oui76Chj\nwk6vHCXMDkHNtwsIf+S0f4KjAu/RIVwzYujZJmaHZuucsBeMC79r2wJoHknVHQ10vugmuN5FaJ2L\n6G4H7HCAw154zfliB81/zUoQcxuB1aGx+9ICJv+zEc2A8hubie50EN3uwJgUx5iydy0jcPVqADJ+\ntQKHq53CWf+gadMXsbobaIgYmjNA4SzbvdE/fybNJxyFdDnJeeUdcl99p9+FP/9hs9BMq++yLkhJ\ntCg/aX93TSNzvnMDzccfRaiqFO+2avJeerNfd8fB0DFvBrWfPx3pMnomzqGqUrZ/90vM/PFN+3ze\n/Gdfo/3wuQRnTsZyOuysHdNi8o13DKkB9sGGEvRxoPnvPlr+lmU3e4gJMo4NUfI/rQO2UxsM0W0O\n4s2JYg4gQxptD2QMKOihtw2qryiwrWwtQWSTE/8TXqr+3oBrRuLia95FHYTWuRJSKIVh4V0cwVE4\nelkI9dfnEvrA2ZWpYhN43kPgRY8dRBTgXR4i74JO3AsSQyDCAZknhck8KYyUEFrnovNFN8JtEXzd\nTdvdmcgoCWGkXkcT3WwQ3uDsefswJsX7XZTuFvayX67Ak7OFho1fIh7JIat0DSXz/oTT3ULNuStp\nOuXonoW/zjnTaDl2EdNu+Fv6HPX0TmVpC20dHcF+zb/2hYaVxyY3y3bohCpLiBTn46pPbis4GDTT\nZNoNfyMweyqBmZNxtHeQ8/p76IMoUDqYUYI+xnSs8tDytyw7dtu1LfCSm/rrcyj9aeuwzy9jIu0v\ndLffeH/U/yw3MXPEFMggNPwmh8q/JJpHeY+IUvRfrTT+Mse+rinwHh2h9P+1DOcW+sUKQ+cLnhS+\n6LYzY/eUNfiKm8Ir/f2mcgoB3sURvIsjNP3JfiNJVYWbgITQeteQw0lCQN7kx8ib/FjC9khBLo2n\nHZOQTmi5XQSnT8K/cA7Z61NnwGS+u9Fu7twHLRoj95V3hjS2dJgug6ZTjqbtyEPRgyEKn36ZrLc+\nTPjximen7jsqTJN4ZsY+CzrYP8a+jdvw9WlsrUiPEvQxpuXvmUnl8TKq0fmsF+vaNrSM4c3SXTNi\naIbE7DMRF26LzJX9z86tqD3DT0YQfjd1Hl/2yhBZp4SI1ejo2RZ69uiuWMnI4BbFpCnofM5D3sWD\ni+O2P5wxsJgDuCR6/tDDSb1DML3pPGT6XgOtXlgeF+39CLojGKby5vvZ/dXPAyB1DRE3yXvhDTJG\nQAAtw8mm/72SaGFuT7ZJcMYkCp5aQ1kvk7Ks9RsIlxcn2wVoGp6dNcMeh2JoKEEfY+LNaQxJhMTs\n0NAyhhd7FjqU/KyFmu/k2707oxrCa2FMjZHzmf7dGIXDTjtMqsAENF/6EIpwgFE1Nk2BtSyJszxO\nbGc/3Xt6GMLDJWWIJfl8QrObdMRbNBx5Qw8rBa5ejetnZ1O38XLatp6FJVuQ529N3jEeJ1JSwMfX\nX4kWiVKw+hVyXns3YXac9+o7+D7eTtuSw7AMJ1lvf4R3hES0ZfkRxApykqxsG1ceR+Gql3sWPAuf\nWkPLcYuJZ/lsUbcsRCxO2V2PJlWrKkYfJehjjOfwCJ3PerqKXvaieeSILSRmLIkw+aF6/I94iTfq\neI8K4zsujBioMbwGWecE8D+UOFsVbouc8/Y9Y2EkEQKK/7uVPd8o6AnzpKoGFbrEd+LgF/x8J4do\nfzCjT9ZO1wPBJe3Tm7azY833bEfJrLMDFP+obdAVupZm0lhWg/+u68FpId/YAt86BBHbDfQRP00j\nOGNyz8w3NKWCztlTqLz9Pwm7GS3tFD3x0qDvc7D4F85J3Sc1bhKYMYmcdXbhkCMQYtYPf0vTiqNp\nW3IYsZxMTJdB/dknIjVBwTOvqkXMMUTloY8xBVf47cVPvXv2KBFui8LvtyV2zxkmzmKT/Es7KL62\njcyTBhbzbgq/3U7GMWGEIdF8FsKQZJ0eJO+i8fda78Z7eJRJ99aT/elOvEeG8S6zx4thgWEhXBYF\n32gf0ltDwdfacRTFSZzVC3BKXNPiuGfG7Li92eUEaQr8D2aw+Zgydny2iPaHvQOactVM2YE/t9W2\n9dWAI9vhmdeRX1wAjU5EIIYWDEE03uVamBhXbzn+KCIFuUP6rvYVZ0u73Se1D1ITdg/VXjgCIbLX\nfUC0KA8zywcug1hhHjVfODO1L4xi1FAz9DHGqIpTdU89LbdmEnrbhbPcJO8SP94jxrfqsxvNgLJf\nthBr0IhVOzAmx/cptDDaGFUmxde00/mCm9Z/+nCUx3CWmHgWRsk6PdjTjm6w6NmSrDODtNySlWjx\nEtNsT5lwCjtfBAQF0a0GDb/IIbLNSdFVqStbI+4wYV8AtL2qLzSQLguWtyLLjifvi7eSM/Mpmo87\nkvalC5LOIUyTwKwpuJqGv3g+EPnPvUbzSUsTN0qJNJy4U3QIqj/nZKy+1gJuF41nHEfxo88P2c9F\nsW8oQR8HjAqTkp+0jfcw+sVZZOEs2r9/CZv+kknrnZnIkP2iGd9jEdvlJPe8ob9NSAlt9/mSQmFA\nv/02eo4Pa7Tf5yP/4o6UNsYxVwRhCaSWOI0XLok8zI8wHPg2biErvInOQ2ZAPJ7Q0ci+CMMq1hkI\ny3DSeNoxtB690BZnywSt1xiEQERjtC1ZQMFziQVRwakVKdvgCcsiWpCLR/mWjwkq5KKYkJitGq23\nZ/WIOdjZQvEmjbaHMoZ8vtAbLtvrJeXFBhcFFoYksiX1Yq0RdieJOdj1AbyRjeaSOH97FYGrV5P/\n3GtJzaW7/ch9H24Z1FiGitQ1Nv/469SdczLhylKiJQXJHYKwzb8ipcnl/a6axmRrAUDqOs7W1G8t\nipFHCbpiQhL60EA4UwhkRCOw1k2sTqf+F9nsOLeIPVfn0XZ/Bv7HvUSrUy9UhDcYqWfnSPQcE++y\nMANlzcgYOIpTZ3YYERdefyai1zWkCYQ1XM+VUvn3hh6HR1d9M5NvuhO9M4gWCiPCUVy1jUy//s/D\nboaRjvYj5hEpLUw0xEqx2quFwnh2JHuQl/znGUSfrBYRiZK3Zh2O4L4ZtCmGzrBDLkIIHVgH7JFS\nnjn8ISnGAxmDzuc9hN41cFbEyVoZHPWc8uHgyDNtQeyLJtF9Fjs/V4wVthcwo5ucBJ71IFx2NkzW\nygBF/5WYneIoiSPcMqmpBjrkfslP9pkhdl1SSHSb046x921Y7ZS4D4n2uxBbsmMSLSX1tBc0IzUL\nT2sm+VvK8fzOn7Bf4OrVZP9qBfMuv47QpFK0SBRXTeOoZot0zJmK5enbsAM7FtX9RcXiOPwBcl5P\n7s5tGpEAAB+hSURBVD6UsXknU353B9UXn0O0IActFif/mVcpu++JURy1oi8jEUO/EvgIyBqBcynG\nAbNDsPtLRcRqdWRIQ7gsmv+UTcUtjbhnjZ7BlpTQ/pCX1jszMds1vIsiSdkpZqfA/6iX0HsGrqlx\nss8J4Ciw0AvNrsrX5JRFK6DZlr49s2H7z+78ev9TXnvx9My9hVa+E0I0/joHMyR7Nc+QaBmS7LNC\naF7JpHsbiHzkJLrNSbxNo/WOTKwO+zreZWFKBqiQ1aRGQW0pBbWlezem8V1PV4g0WhjNbYhoLLlA\nKG6ixWIIS5L9xnuU3fdEj896X7Le3cjcq36OZTgRsfiovU0o0jMsQRdCVABnAD8FvjMiI1KMOS23\nZhHbrSO7vFFkRENGJHU/ymPyA6O3mNV0YxZt9/t6Kmc7n/MQfM3NpPvqcZaaxBs1dp5fjNUpkGGN\ngGHRckcmlTc30vGsx079tPpEDQWENzrThE9sZEij7uc5aJkWvuPscIDmhsrbGqm9No/IFicCMKbE\nKPlZC5rXFiYhwD031lP2n/uFTuL1OprPQs8cHfEaK2HPW/MW9Z9akRhUsiwcwRBzv3E9Wqo+o2no\n3dJOMbYMN4b+O+D7JPXyUkwkOlZ5esR8L4JYtSPBA3y49J6wmX5B2719bBAsgRUWtN5pNztuvCkb\ns1Xr2UdGNWRAo+5/cgm/aySYc/WM2i3R3IMQ15BGzQ/yaL5tb2NlY1L8/7d35+GR1lWix7/nrX3N\nnu6ku+mmWZQW4YKNbKKyiAgKojOKIPK4MSqbiKi4jTPjc11wFAaBR2h0RBFEBjdcRpTlOipoL1y5\ngEDbbJ3udNbKUvtb7+/+8SbpVFclnaSSVCp1Ps/jI2R565ciOfWr857fOay9o4f1v9rNgb/czdq7\negisn/q0o1jg6ygsWDBfTL6hEdZ/ZRO+gQRWJotkcwR29XDwv940q2CuqmvOO3QReTPQY4zZIiKv\nn+brLgYuBmhdWX7SuKqyKX4LjJn6czNlHHcQxuDtMZxhC/9BNu1XJ5CAcdsM7NswzBbSj7l5iOTv\ng2UrTHI7fMTfnCS9zZTsxE1KiL0jSeLO0p45pReyGLg1TuM7kniie4PyUqu7LwwJLzY/Qnqbn0jf\nD2k79AcEYi/N++NEn36ODZd+kWxnO2IXCPTMvbHWODsSYmjj4Rifj9hjTy1KDX09q+TP9UTgbBE5\nEwgCcRH5vjHm3ZO/yBhzC3ALwPoNR9T+VmYZajgn6Q54ntycyjIEX56ruFd77/Vxhn60N62S+7uP\nritaWPmlAbdN7b7E4Fvj7oqldCbEhMbzRhn+WZnyRAODt8cJHZsh/Uhw2tQLAF7IPuMjfHTlNff5\nXR5GHwyBgcjr0vjXVL6zze/x8OIF7ThJwWQtUt6L6P/7Ozjo9RcTbd9S8fUN0P/6V9N3xmsohEPE\ntz7Bynt/i2+48pPBiaM38MJl70aMwYjAu9/CinvvZ+XPHqj42qq8Ob+fNsZcY4xZbYxZB5wHPLBv\nMFe1oek9IwSPzLnzNf0OEnbwtBTo+N+VtcF10sLQpBz5OJMVhu6JED42i+wzxk0ChuaL3MMzDW+b\nNDJunNcQPj7DyK/DUyT63GP5ma0BGt45WnYYdNFa8uBtrXxHnrg7wvNvX0nvDXF6b2jghXesYOD2\n6P6/cT/6b4xTGLL2vtjaglMI8/wz39lvq4GZ2HnRW9n1nnPIHNBJvrWJ/pOP4+kvXYkdCVV03UIo\nyAuXvRsT8OMEA+4ADL+PPeeeRmqdvlNfKFqHrrD8sPrmPlbf3EfbR4fo+OIA6+/rnvXx+X3ZPR4o\nW/Yt5Hb46PjyANHT0ojPTb94V9h0fGVg4qZjy/tHCG3MIgH3RUZCDv51eSLHZkjcFWW6I5wmI+Rf\n9BI42J7UN6fkqwi+zB1oXYn8bg+932hwq2hyFuTd3XT/zXFyL1SWs0r+oXzaye72YmebK7p2vjHO\nwMnHFjfh8nkphEP0n3JcRdcePuqwshOXjM/L4GuOrujaamrzcvTfGPMQ8NB8XEtVhwiEjsgROmL+\njvt72wtQ7jVBDP6D8lghQ8cXB3E+k8BJC54mp3i6kA9W39BP9lkv2Wf8+FbZBI/M8fzbV+w/P45g\n93o44Ls9DP04Qt9NDZhkcS/14CuzdF5X+TCO0YdCZc8cmYIw+rsQze+b+3F9K2wolEk7GyBz1d3k\nwmbOFTCpdasQ2y4pVTQBP71vOomBk15F+LkuVvz0twR3zW6OpylzynScM83nVGW0l4sC3JuX6W1+\nnBGL0JG5sv1IZssKGRrfNUriruK0iwQMrR8aLvq66cbvBQ6xi8bfOYkZvLG0DOHjMlgBaDovSeM7\nk6S3+sk86Uc8EHl9Gn/n/FRvmALl0x9mio9PwUkJTlLwtO59YWt45yj9N8WLX8B8hsgJmYlyyrmW\nNvoGh8Aq81wagx2PYTfGyXa0MXTM4Rz8bzcRfq5rxtd2JyqVBm4rl6epzMEkNT805aLIPefluTNX\n0nVFK92fa2bHmzqKyvkq0XrpMC0fGsbTXADLEDg0x6ob+gi+Yu61yqFjskVdC8ty3GqYcSLuyLzm\nC0dpOn90TsF83+Cc3+Nh52Ut9F3XUGYkHojXEBvryZ7b6WH4lyGSjwZKTrg6KWH3NU38/eROnntL\nBzvOWMnow+6pzaZ3jRI9Ne22M444SNAhcGiOlV8ofWcxHthnKvzCLrcHi71PykkErLGfx+PBCQbo\nuvCts7q2b3iUVbf/FMnm3OuP9aJp+p+t8zJRSZWnO/Q6ZwzsvLQVu9cDRiYyBwOb4oRemSd8TGVD\necWC5veM0vye+eun3nrpEKk/BXEyjA2kGF/15KAqpDcHyD7rLRluPVupRwP0XNtIbocXK+7QdOEI\njReM8tJFbdh9nkmVNGPr8LjBvPmDw/jW2ez5YiND90UmXoQ8cYc1m3rxr3Yj++5PNZP6c8Ad2AEU\ner3svqaZNZt6CW7I0/Fvg+Q/PEz2GR/ejsK8nt496Cu38vwl55M87CBwHDf9UqaHS+qgNbO+dusD\njxB9cjuDJxyN4/fSuOUJws++oAMvFpAG9DqXecJHYciadNzdZTJC4u5IxQF9IfjXFFj7wz0M3B4l\nvS2AMyrYu8p3OUw/HiBwiI0xkH3ah8kIgQ05rGlKIou/30/XlS0TKQ9n2MPAbXHSf/VTGLX2KYsU\n8DnETsnQ8k/D+NfZDP8izNB9Ycjt7adeyAg7P9LK+p/tId/tcYN5rrQSaOA/Y3R+1d2J+zoL+Gbw\nrmK26RfvSJKDv3wrdiyMHQzy9FeuwpSZVORJTj+PdirB7j467v3NnL5XzZ4G9BpnDKS3BEht9lPo\n8yAxh+AheaKnpie6903HSVruoIWSz4gb6KvI7rUY+W0YkxbCJ2aKdqa+jgIrPum2Ze2/LcbArbHS\noOiAhByyO7x0Xd5KYdD9WQFWfGGA2Kn77wLY/63Y2HCLSdfNWKT+OEWNuy34D8zjX+e+Kxi8M+JW\nvhQR7J1eMn/zYrIW4qe0Jt8I+Zfm/uc5+8CewjuSovX+P9J3+olFXRclk6VtAcbcqfmnAb2GmTx0\nXdFK+jH/pKAjEHDwXN/AAd/txbdy+l1d6JU5TJmMhAQdom+Y+UzO+TbyuyDdn3XL8owtyKYY8bOT\nNJybov+mOJkn/fg6bVouHqHh7CQD346VXiQn7PliE5bP4IxYRSml7s82Ezi4B//a6dMxbh6+TOD2\ngPhMSbCXkCFwyN4XHrtn6j+x0YfCNF0wMpFqKeI1hI6q/N3RbAN7592/ohCLMHjCUW4FjNdLy0N/\npv0XD1e8FrXwNKDXsMS9kbFgvs8OMGtR6BN6vtTIquunP75thQ1tVyfo/WqjG1gcQYIO/rU2DWcn\nK15j8tEAQz+OYDJC7IwUsdPSZeebOmnB7rfwthagIHR/rrno5KopCEM/jTD8kygmDxih0O9h19U+\n2j89yOqb+th5eQtmxGJvABZIC07GlKaUbGHo3ghtU4yMGxc4OI/d7aFcUPe2F8jvkr2Dpb0Gb2uB\nyEl7d/7+A/Ok+6yy3y9egydmaHzXSHElkOVW/TTN432HmZKCwwG33E3nnfeRa23G39OPN1m9F3Y1\nOxrQa9jwTyNT12MbIfmHoJt22E/mpPHcFMGX5Un8KEph0CJ6cprYGakZpWym03tD3A1UaTd/nPpL\ngOGfR1h1Q9/EmowDfd+Mk7gz6tZcGQi/JoMpt+bs+A570pCIjEXfNxpZf/9ufB0FciNlapzLFcQU\nBLtv/ymlln8aJrU5ULQTl6BD7Kwk/lUFRn8fJPu0HwRip6Vpu2IIPJDaHGD0wSCexoK73H3WIH5D\neKO7A2+9bBjfWpvE7TEKCYvQMVlaLxna77ur2ZhrCkbVFg3otWx/5QKzKCcIbsiz8p/nr3FSfpeH\nxB2xouZbJm2RfsxP8g9BomO72IHvRN2gP2k3nnq4zKCFCaU/lJO0KCQsZBbnVSTkFO2kpxJ8RZ5V\nN/TRe20j2e0+PI0O/kNyjPw84i5l7EWo48sDRF+bwRjo/nwTow+E3BeB8eV6zMSJTwk4hF+dJXik\nmzgXgcZzUjSes/ABNHn1/YvWY10tPq1Dr2Hxc5JIcIoDQJYhclJmv7vzhZL6c6DskXuTtkhOCtiD\n34uX9nrJW2Xruqd8gbIMVtSh4W3lng+DRI3bp2b8MmMppex2L8+ds4Ln/3EFg3dGyt5LALd+fe1d\nPRy6uYvO6/rI/F+3KsVkLUzabe+7+1PNOEkh9WjADebpscohRybSPYENOYJHZGn/ZILOf+8vVx24\nKJJX3z/rmnVVG3SHXsMaz02SfDhEepu/+OZcwOBpcGi+aBhjUzZnvdCsmCkfgL0Gq8ENrsYBZ3iK\nqGaB+Ma+zhbEawgenSWzLVB86jTo0HBuEsvvdo1M/iFA6pEgpiBujxgvrP5WL/ZuD4m7ozgpIfqG\nFEP3Rkh8f29lTN8NDaQ2B1j179O3Ahj5Rbi05e/YepN/CLoHh9Jl8uUBQ9P5I8TP1Hy0Wjga0GuY\n+GDVN/tIb/WT3hrAHrSwAg7JR0LkdvjY+ZE2xG9ovyZB/PTFDSSRE9OI1VSSvhaPoeFsN7UgFvjW\n2eSfL60hDxySp+1jCXqubSTf5cW3skDj25PYJ2Xov7HBPW1pIH52kraPujc2xQurvj5A5gkf6W0B\nPK0Foq/LuG0FXpYn+no3xTL83yHsbm9RmaPJWKT+FCT7jI/AoVMf3HFvHE/xORusgHHf9+7zNSLu\nf6+lZLHH3KmFpwG9xo0faQ+/ys3HvvT+sUHGecHkBZOGPV9owtdpEzp88UaDWUFYdWMfXZe3TFSB\nmAKs+OxgUalg+9UJdn2sZWzep3v3UIKGxvNH6Ppoq/vOwwi55yy6P9tM2xVDHPTALuw+D55Gp2wP\nmOAr8tO2FkhvCbgpkXKf+6t/2oAee2Oa4V+FS3fhBSFyQhb/Opuhn0RKa9cdiJy4/5x9NWhgXz40\nh17jnLSQ/GOA1KMBsjs8ZJ70leSfTVYY/F6ZOu0FFnpljoN+s5vOr/fT8eUBDvrt7pKUQ+T4LKtv\n7iN8bBZPm034+Ayrv9XH6MOhiWA+zmQs+m5sANyDRdM19JqOd6Vd0ocdAM9Yh8jpfqaNWWKnp91c\nvRjwGiTg0PaJQTyNDsENeZo/MIz4DRIca/sbdOi8tn+imdZSpXn12qc79Bo28kCQ7s817z3paSj/\nEm2E/K7q/KcWH/ttHxD6XzlW39yHMWDv9iBBQ+Zxf0ntOLi7/Pwez0QflKmMPhRk4PYYhQGLyIkZ\nmt87MjHIouHsFAPfjsPk05mWwQo7RE6YfhctAis+P0jDW5OMPhzEChpiZ6TwH7B3PS3vGyV+ZprU\nnwJIwBB5baZoxJ0qlkutoG/7P5IdWUe0bQvNB/4Uj09LJudCA3qNyu/20P3ZZkzG2idPXSZw+B3C\nxy7Nt/vjUpsDdH++icLgWHWId4oAWJD9jsXr/3aUgU17q2cSu7yM/CbM2rv34G1y8LY6rL6xj92f\nbnYfz3GP63d8tX9GN5BFIHRkjtCRU/eO960s0HBu7QWlxU6/JPuOZPuDt2EcL8YJMNR1Mnue+iAv\ne+M/4AtW3qu+3mhAr1HDvwpjykyywQuIA/mxrbrH4IkYms5f/FOHxobCkIUn7kx7QzDf5aHr8pbi\n8kUbN6UxaZcuAYfYm1JYkal3u4VRYeDWePF8VFsoDAuDd0Rpu9Ttwx46MseB93WT7/IgPvCt0Mn2\nky1GYDcGXnjkSzj23tmwphAmn/bS/filrDnmXxfssZcrzaHXKGdYoMy9O7EM8TPSBDZk8XbaNJyb\nZO1de0om2TtpYeR3QYZ/HaIwaWCEkxIG74rQdWULPdc2zGmEmjHQ/59Rt7/3WR1sP7mT/k3RKYc9\nJO6JYOx9XpycsbLDcMHNRfsN8bNSrLgmMe1j5571lX/xyFukHik+sCQC/tUFDebTWMi8up1pIZfs\nLP2E8ZPYedqCPe5ypjv0GhU5MUviR9HSaguB5veOTHT7Kyf5SIBdH2/ZeyS9ILR9fJDYG9K8cMEK\nCv3uYRk8hqEfR+i8dmBWFRpDP4owcMukA0M5of9bDWSe9LPyc4mSaUj5nd69/VAm88KKzyQIHZ3D\nEy9f0bIvT0vB7fVSwuCMCsa4gdzkoZCw8DRO/+5hXHqbn56vNpJ91uf2RL9ghOb3jlbt4NZiWqjT\npZYny1SnxSzP0k4RLlV18Ou4PIU2Zgkflyk+ARlyiL81OW0wL4wKu65qwaQsTNJy/z8r9H6tkd7r\nGrB7rb2BuCDuKcjPNGFmMZGu/7ZYaY+ZgpB8KMSOt6wk80RxBA1tzJY/8WoLwcNz+FbMvKLFf0CB\nwGF5Su8lCPluD6MPBum/Lcr2kzt57uyVbD+lk/5vT/3uASDzNx87L2l1e7Y4gpNwe6L3fqNhRmta\nDhbidKnHP0q07S8gxa/A4knTevBd8/pY9UIDeo0Sgc6vDrDyC4NEXpsmemqKjq8M0P6J6bsHJv9P\nsOymyNjCyAOhMr27wRm2GLk/NOO1FfqnaqoimJTF7mtaigJow1tS7q7dt/eDEnSInp7Cv2b26ZDW\nKxLlN345i97/aGDgtvjYC5n7ojawKU7ih5Ey3+DqvzU2Vie/l8lYDN0TpTBaX/N35juorz3+kwRi\nL2B5k1jeUcSTJt7xe9pf/t15fZx6oSmXGiYeiL0hTWwWfcudjFX+pKPjXq/8RlUY/F6U+Btn9jj+\ndXbRPM992b0W9i4PvlVusLbChrV39NC/KcbogyGskKHhnaM0vn1u7XvF417TSZYGW7vLO9Eka5zJ\nWAzcFqfpvPKPl3u2fAklXoPd7cFzcGUj7haLkxZMVrAanIr6yMznDVNfqJ/DznwLyd5XkUt2Em5+\ngmCDzhydKw3odSZyfIZep7Hk4xI0xM9Kkvh+jHLb29zfZ35uve2q8dOfU7f2ZZ9NvKfRof3jQ7R/\nfPp3GDMx1UlPCTglO+1xhcGp36z6D86T7/KUBnVb8M5ji9uFUhgRuv+lieTv3XdZvpU2K/55kPDR\nU5ddLiYRiLZvAbZUeyk1T1MudcbXUaD5A0NuztoygNuJMPq6NC2XD0/5Er/vjczpRI7PsuqGfrwd\nNqWNwA2+tfl57fW9L8sP7Z8bnPQzuikcX2cB3wHld9O+aSYXtXxwGAkU/xwSdGh422hNHBjquqzV\nDeZ5gbyQf8lH16Wt5F6aRb/hMrRr49KjO/Q61PKBUcLHZRn+eQSThdjpacLHZxGB5otGGPx+cX9y\nCTo0v3dkVo8R3pjlwJ9003VlC+ltAUzBbZ5lBc3E4OOFFD89TWC9O7TD3uMhclKG+FlJ0luC7Lq6\nuaRjY/vHpi6HDB7m9kTvubaR3LM+rJhD0wWjNL9vds9JNWSf9ZJ9pkw7CFtI3Bnd7z2XmdBeMEuH\nBvQaZ/KQ+nOQwrAQelUWX/vMdtKhw/OEDi8NYi0fGsZJCkM/jrr9zA00vWeEhn+YfT5bfLDqhn4y\nT/jI/DWAd0WByElpLP/+v3ey0YeDDNwWI9/tJXhEltaPDBNYv/+8deBgu6RuPXJihlXX99N3U5zc\n817862xaLxmemB40lfCrcqy7q2ei7LFW5Hd5EW+ZeyO2kCvT5bISOjyj+jSg17DsMz52frgVk3Pr\nq7GFpgtHaL1keM7XFA+0f2KI1kuHsfs8eNttrOkGCO3vejL+4jG3To+Je8L0fr1xYkedfChE6pEg\nB9zeM6OgXk74mCwHfKd3Tt9bS8Ec3PsJpkyqXALOvAyh3pcG9erSHHqNMg7svKyFwqCFM15PnhMG\nfxAl+acKh4HiVon4D6gsmFfK5KHvPxqLa9odwWSE/pvj1VtYDfF1FIiOd4ccNzaEunEO77pmQvPq\n1aMBvUZlHvfjJEunyZu0ReKeqWuqa4nd4yk/Fs4R0n+t/EWrXqz850FaPjyMt9PGaiwQOyPFAT/o\nmdWN7tnSG6bVoSmXGmUy4h5hL/M5N9DXPk+j487kLMO3ojZqv5cC8UDzhaM0X7j4Ddo0BbO4lsdf\nfh0KHpErexxfgg7xM2qvbWs5VsTtNS6B4h9Ugg7NH1j6FSbKpTv1xaMBvUZZIUP7Z8ZqrT1jtdYh\nh8CheWJnLo+ADtD+6UFiZ6QnJgBZMYe2qxJEX6vNm2qJpmAWx5xTLiKyBrgdWIl7mPwWY8z187Uw\ntX8NZ6YJvjzP0L0RCgMW0ddliJ6SXnLDiCth+d0ccPvVCQoJC29bYVn9fPVGUzALq5Icug1cZYzZ\nKiIxYIuI3G+MeXKe1qZmILDenpfj8kudFTZY4aV/zF7tnwb1hTPnlIsxZrcxZuvYP48ATwGr5mth\nSqnlS1MwC2Necugisg44Cnh0Pq6nlKoPGtTnV8UBXUSiwH8BHzXGlBxRFJGLRWSziGweGdShr0qp\nYrpbnz8VBXQR8eEG8zuMMfeW+xpjzC3GmI3GmI2xpuZKHk4ptYxpUK/cnAO6iAhwG/CUMebr87ck\npRZW8tEAL32glR1nrmTXJ5vJ7tDzdUuFBvXKVLJDPxG4EDhFRB4b+9+Z87QupRbE0C9D7LqyhfTW\nIHa3l9HfhXjxwnay2zWoLxUa1Oduzr/Fxpj/YaqR3UotQaYAfV8r1+wL+r7ZwKrr+qu3OFVEe6zP\njZ4UVXWjMGDhpMtNyBYyj8+ySbtaFLpbnx0N6KpuWDGn/LBnwNOqh5aWKg3qM6cBXdUNKwjxNyfL\nNvtqeb82+1rKtLRxZjSgq7rS9okEsTeONfsKOUjYoeUjQ8ROT1d7aWoGNKhPT2/tq7pi+WHlFwZp\nuypBYcCDt8Oe9YxTVV3aC2ZqGtBVXfLEDJ6YDsmoVVoFU56mXJRSNUtTMMU0oCulapreMN1LA7pS\nalnQoK4BXSm1jNR7UNeArpRaVuo5qGtAV0otO/WaV9eArpRatuotqGtAV0ota/W0W9eArpSqC/UQ\n1DWgK6XqxnIP6hrQlVJ1ZTkHdQ3oSqm6s1zz6hrQlVJ1a7kFdQ3oSqm6tpx26xrQlVKK5bFb14Cu\nlFJjan23rgFdKaWWCQ3oSim1j1rdqWtAV0qpKdRaUNeArpRS06il3boGdKWUmoFaCOoa0JVSaoaW\nelDXgK6UUrOwlIO6BnSllJqlpZpX14CulFJztNSCugZ0pZSqwFIK6hrQlVKqQkslBVNRQBeRM0Tk\naRHZLiKfmq9FKaVULap2YJ9zQBcRD3Aj8CZgA/AuEdkwXwtTSik1O5Xs0F8NbDfG7DDG5IC7gHPm\nZ1lKKVW7qrVTrySgrwJemvTvO8c+VkRELhaRzSKyeWRwoIKHU0qp2rLYQd1bwfdKmY+Zkg8Ycwtw\nC4CI9J5/9JoXZvk4rUDf7Je37OjzoM8B6HMA9fkcrJ3JF1US0HcCayb9+2pg13TfYIxpm+2DiMhm\nY8zG2X7fcqPPgz4HoM8B6HMwnUpSLn8BDhGRA0XED5wH/Gx+lqWUUmq25rxDN8bYInIp8N+AB/i2\nMeaJeVuZUkqpWakk5YIx5pfAL+dpLVO5ZYGvXyv0edDnAPQ5AH0OpiTGlNzHVEopVYP06L9SSi0T\nSzqg13trARFZIyIPishTIvKEiFxR7TVVi4h4RGSbiNxX7bVUi4g0isg9IvK3sd+J46u9psUmIleO\n/S38PxG5U0SC1V7TUrJkA7q2FgDABq4yxhwGHAdcUofPwbgrgKeqvYgqux74tTHm5cCR1NnzISKr\ngMuBjcaYw3GLMc6r7qqWliUb0NHWAhhjdhtjto798wjuH3DJadzlTkRWA2cBm6q9lmoRkTjwWuA2\nAGNMzhiTqO6qqsILhETEC4TZz9mXerOUA/qMWgvUCxFZBxwFPFrdlVTFdcAnAKfaC6mi9UAv8J2x\n1NMmEYlUe1GLyRjTBXwNeBHYDQwZY35T3VUtLUs5oM+otUA9EJEo8F/AR40xw9Vez2ISkTcDPcaY\nLdVeS5V5gaOBm40xRwFJoK7uK4lIE+679AOBTiAiIu+u7qqWlqUc0GfdWmA5EhEfbjC/wxhzb7XX\nUwUnAmeLyPO4abdTROT71V1SVewEdhpjxt+h3YMb4OvJacBzxpheY0weuBc4ocprWlKWckCv+9YC\nIiK4OdOnjDFfr/Z6qsEYc40xZrUxZh3u78ADxpi625UZY7qBl0TkZWMfOhV4sopLqoYXgeNEJDz2\nt3EqdXZjeH8qOim6kLS1AODuTi8EHheRx8Y+9umxE7qq/lwG3DG2wdkBvLfK61lUxphHReQeYCtu\nBdg29NRoET0pqpRSy8RSTrkopZSaBQ3oSim1TGhAV0qpZUIDulJKLRMa0JVSapnQgK6UUsuEBnSl\nlFomNKArpdQy8f8BuWMG8yLBkJIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cfd7025f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = gen_two_clusters(center=5, dis=1)\n",
    "svm = LinearSVM2()\n",
    "svm.fit(x, y)\n",
    "print(\"准确率：{:8.6} %\".format((svm.predict(x) == y).mean() * 100))\n",
    "visualize2d(svm, x, y)\n",
    "visualize2d(svm, x, y, True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mini-Batch 梯度下降法（MBGD）\n",
    "\n",
    "+ 上述解决方案已经不错，但我们还是有些太“激进”了——我们每次进行梯度下降时，选取的样本点都是使得损失函数最大的样本点，但一般而言使损失函数最大的样本点如果不是关键的样本点（支持向量）的话、通常而言会是噪声。当数据集比较差时，噪声所带来的副作用很有可能就会盖过支持向量带来的正效应\n",
    "+ 为此，我们应该引入一定的随机性。神经网络的训练中所用的 MBGD 就是很好的方法：每次都从数据集中抽样出一个小 Batch，然后用这个 Batch 来做梯度下降"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class LinearSVM3(LinearSVM):\n",
    "    def fit(self, x, y, c=1, lr=0.01, batch_size=128, epoch=10000):\n",
    "        x, y = np.asarray(x, np.float32), np.asarray(y, np.float32)\n",
    "        batch_size = min(batch_size, len(y))\n",
    "        self._w = np.zeros(x.shape[1])\n",
    "        self._b = 0.\n",
    "        for _ in range(epoch):\n",
    "            self._w *= 1 - lr\n",
    "            # 随机选取 batch_size 个样本\n",
    "            batch = np.random.choice(len(x), batch_size)\n",
    "            x_batch, y_batch = x[batch], y[batch]\n",
    "            err = 1 - y_batch * self.predict(x_batch, True)\n",
    "            if np.max(err) <= 0:\n",
    "                continue\n",
    "            mask = err > 0\n",
    "            delta = lr * c * y_batch[mask]\n",
    "            self._w += np.mean(delta[..., None] * x_batch[mask], axis=0)\n",
    "            self._b += np.mean(delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 测试"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top n LinearSVM 准确率：    63.0 %\n",
      "MBGD  LinearSVM 准确率：    69.0 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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zsiy7w5tog7R4T5em13YkXD25BXqGDxSX3ykMoRFMAB1KMjY0NIbSzq0roIb3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cfd77db70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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psgJzLYfo4qIHy48kkkGhQ+whmUw2cJTR0i3SqjRKuA3D2AU0yoSXnHvyjsB7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\n6cIlJv1lOgsmm5ZLLbo05dnJo2kY6706vhU6VaKU+h6YoLV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      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cfda0cfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 进一步拉近正负样本点间的距离以观察性能\n",
    "x, y = gen_two_clusters(center=5, dis=0.5)\n",
    "top_n_svm = LinearSVM2()\n",
    "top_n_svm.fit(x, y)\n",
    "print(\"Top n LinearSVM 准确率：{:8.6} %\".format((top_n_svm.predict(x) == y).mean() * 100))\n",
    "mbgd_svm = LinearSVM3()\n",
    "mbgd_svm.fit(x, y)\n",
    "print(\"MBGD  LinearSVM 准确率：{:8.6} %\".format((mbgd_svm.predict(x) == y).mean() * 100))\n",
    "\n",
    "visualize2d(top_n_svm, x, y)\n",
    "visualize2d(mbgd_svm, x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 存在的问题\n",
    "\n",
    "Top n LinearSVM 和 MBGD LinearSVM 各有优劣，很难直接说谁好谁坏；但它们都有一个共同的问题，那就是它们所运用的梯度下降法都只是朴素的`Vanilla Update`，这会导致当数据的 scale 很大时模型对参数极为敏感、从而导致持续的震荡（所谓的 scale 比较大，可以理解为“规模很大”，或者直白一点——以二维数据为例的话——就是横纵坐标的数值很大）\n",
    "\n",
    "可以通过下面这个栗子来直观感受一下 scale 很大的数据所带来的问题："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top n LinearSVM 准确率：    50.0 %\n",
      "MBGD  LinearSVM 准确率：    50.5 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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Ny7ZSU1lDTWUtDqeDBV+YS9+cLEZMHcrF1+d1S2JvThO9Ukq1g7ve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\nNNErpVSU00SvlFJRThO9UkpFuf8Pj62OXKR9yioAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cfd78a978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0IQIrY1y9/cvZzRlsJNOIi+hJB5pV+nsVoiKS6ENIcR3+b3OJaRBdJ+rwFTmf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\nECLM/T86PUJjXFPIzwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cfd99c898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 将 scale 从 1（默认）调成 5\n",
    "x, y = gen_two_clusters(center=5, scale=5)\n",
    "top_n_svm = LinearSVM2()\n",
    "top_n_svm.fit(x, y)\n",
    "print(\"Top n LinearSVM 准确率：{:8.6} %\".format((top_n_svm.predict(x) == y).mean() * 100))\n",
    "mbgd_svm = LinearSVM3()\n",
    "mbgd_svm.fit(x, y)\n",
    "print(\"MBGD  LinearSVM 准确率：{:8.6} %\".format((mbgd_svm.predict(x) == y).mean() * 100))\n",
    "\n",
    "visualize2d(top_n_svm, x, y)\n",
    "visualize2d(mbgd_svm, x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通过下面这张动图，我们能够直观地感受数据的 scale 很大时 LinearSVM 的训练过程：\n",
    "\n",
    "![Failure of LinearSVM][2]\n",
    "\n",
    "可以看到，模型确实一直在持续震荡\n",
    "\n",
    "[2]: https://cdn.rawgit.com/carefree0910/Resources/83441596/Lines/LinearSVM(Failed2).gif"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 解决方案\n",
    "\n",
    "+ 采用更好的梯度下降法，比如`Adam`之类的\n",
    "+ 进行数据预处理、把数据的 scale 弄回 1\n",
    "\n",
    "关于`Adam`等梯度下降算法的实现和在 LinearSVM 上的应用可以参见[这里](https://github.com/carefree0910/MachineLearning/blob/master/NN/Basic/Optimizers.py)和[这里](https://github.com/carefree0910/MachineLearning/blob/master/e_SVM/LinearSVM.py)，下面我们就仅展示进行数据预处理后的结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 1 LinearSVM 准确率：    98.5 %\n",
      "Top n LinearSVM 准确率：    97.0 %\n",
      "MBGD  LinearSVM 准确率：    97.0 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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GIyqBGJlC3waZ3xfIUIykSXPnSzez4uu1zHtpPiOnD0H0ffEtORSygaOcJpcoWjCCrkQQ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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cfda69550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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se0emZPpcDoNudF+6WBWr58JfD0uhLZCdqx+NgWv/gTa1L0N3IapjBO9ufYnb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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cfda620f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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owghy0gUyotKY0Fqpu++tcscfgIuBCEVRTgPTNU37zBtrS7zLlR9CyxGw5WOx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cfda620b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = gen_two_clusters(center=5, dis=1, scale=5)\n",
    "# 进行归一化处理\n",
    "x -= x.mean(axis=0)\n",
    "x /= x.std(axis=0)\n",
    "# Top 1 梯度下降法即为极大梯度下降法\n",
    "top_1_svm = LinearSVM()\n",
    "top_1_svm.fit(x, y)\n",
    "print(\"Top 1 LinearSVM 准确率：{:8.6} %\".format((top_1_svm.predict(x) == y).mean() * 100))\n",
    "top_n_svm = LinearSVM2()\n",
    "top_n_svm.fit(x, y)\n",
    "print(\"Top n LinearSVM 准确率：{:8.6} %\".format((top_n_svm.predict(x) == y).mean() * 100))\n",
    "mbgd_svm = LinearSVM3()\n",
    "mbgd_svm.fit(x, y)\n",
    "print(\"MBGD  LinearSVM 准确率：{:8.6} %\".format((mbgd_svm.predict(x) == y).mean() * 100))\n",
    "\n",
    "visualize2d(top_1_svm, x, y)\n",
    "visualize2d(top_n_svm, x, y)\n",
    "visualize2d(mbgd_svm, x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看到在归一化处理后，即使是简单地采用极大梯度下降法，也能够在比较苛刻的数据（`center=5`、`dis=1`、`scale=5`）上表现得不错"
   ]
  }
 ],
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